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# Fall 2013 (Total Marks 15)

February 07 23:59, 2014

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### Objective(s) of this Assignment:

This assignment will strengthen the basic idea about the concept of the following distributions:

• Poisson distribution
• Binomial distribution
• Hypergeometric distribution

Assignment No: 2 (Lessons 27 – 30)

Question 1:                                                                                             Marks: 4+4=8

a)     A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

b)     In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

Question 2:                                                                                             Marks: 4+3=7

1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?
2. The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

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a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

K = 4

N = 10

x = 2

n = 3

P(X=2) = 0.3           Ans

b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

P = 0.36       Ans

n = 100        Ans

a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

a).A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

K = 4

N = 10

x = 2

n = 3

P(X=2) = 0.3           Ans

b).In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

P = 0.36       Ans

n = 100        Ans

a).It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

b).The average number of accidents occurring in an industrial plant during a day is 3. Assuming Poisson distribution for the number of accidents (X) during a day, compute probability that at most two accidents occur in a day.

Question 1

a)      A batch of 10 gaskets contains 4 defective gaskets. If we draw samples of size 3 without replacement, from the batch of 10, find the probability that a sample contains 2 defective gaskets.

Solution:

When n is greater then 5% of N the hyper geometric formula should be used.

Given:

K = 4

n = 3

N = 10

X = 2

putting these information in formula of hyper geometric

ans. is 0.3

Question 1:

a)      In a binomial distribution, the mean and the standard deviation were found to be 36 and 4.8 respectively. Find the parameters of binomial distribution.

Solution:

There is two parameters in binomial p.d. that is n and p and it’s generally denoted by b(x; n,p)

In binomial distribution Mean = E(x) = np

And     S.D. =square root npq

Given:

Mean = np = 36

S.D. =  = 4.8

Equations:

np = 36…………(1

square roor npq= 4.8………(2

For finding the value of n and p

First put the value of np in equation (2)

(square root q36) = 4.8

(root q)6 = 4.8

root q = 4.8/6

root q= 0.8

q = 0.64

We know that p+q = 1…………(3

For finding the value of ‘p’  put the value of q in equation (3)

P+ 0.64 = 1

P= 1- 0.64

P = 0.36

Now, for finding the value of ‘n’ put the value of p in equation (1)

np = 36

n(0.36)= 36

n = 36 / 0.36

n = 100

So,

p = 0.36

n = 100

Question 2:                                                                                             Marks: 4+3=7

1. It is known that the computer disks produced by a company are defective with probability 0.02 independently of each other.  Disks are sold in packs of 10. A money back guarantee is offered if a pack contains more than 1 defective disk. What is the probability of sales result in the customers getting their money back?

is q mai hum binomial formula use kary gay kyon k poisson ki condition satisfy nai ho ri.

poisson k ly 'n' ka 20 say above hona zarori ha

so binomil lagao aur slove kar lo :)

question 2 (b) mai poisson process wala formula use ho ga kyon condition mai physical thing ki bat ho ri ha aur trails b independent hai

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